On the Hyers-Ulam Stability of Differential Equations of Second Order (original) (raw)

Hyers–Ulam stability of linear differential equations of second order

Applied Mathematics Letters, 2010

We prove the Hyers-Ulam stability of linear differential equations of second order. That is, if y is an approximate solution of the differential equation y + αy + βy = 0, then there exists an exact solution of the differential equation near to y.

Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

International Journal of Mathematics and Mathematical Sciences, 2009

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second order y p x y q x y r x 0. That is, if f is an approximate solution of the equation y p x y q x y r x 0, then there exists an exact solution of the equation near to f.

On Hyers-Ulam Stability of Nonlinear Differential Equations

Bulletin of the Korean Mathematical Society, 2015

We investigate the stability of nonlinear differential equations of the form y (n) (x) = F (x, y(x), y ′ (x),. .. , y (n−1) (x)) with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

Hyers–Ulam stability of linear differential equations of first order, II

Applied Mathematics Letters, 2006

Let X be a complex Banach space and let I = (a, b) be an open interval. In this paper, we will prove the generalized Hyers-Ulam stability of the differential equation ty (t)+αy(t)+βt r x 0 = 0 for the class of continuously differentiable functions f : I → X, where α, β and r are complex constants and x 0 is an element of X. By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order.  2005 Elsevier Inc. All rights reserved.

On the Hyers–Ulam stability of the linear differential equation

Journal of Mathematical Analysis and Applications, 2011

We obtain some results on generalized Hyers-Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known estimates of the difference between the perturbed and the exact solutions.

On Hyers-Ulam Stability for Nonlinear Differential Equations of nth Order

International Journal of Analysis and Applications, 2013

This paper considers the stability of nonlinear differential equations of nth order in the sense of Hyers and Ulam. It also considers the Hyers-Ulam stability for superlinear Emden-Fowler differential equation of nth order. Some illustrative examples are given.